If in a right angled triangle, `a a n d b`are thelengths of sides and `c`is thelength of hypotenuse and `c-b!=1, c+b!=1`, then show that `(log)_("c"+"b")"a"+(log)_("c"-"b")=2(log)_("c"+"b")adot(log)_("c"-"b")adot`A. 1B. 2C. `(1)/(2)`D. none of these

If in a right angled triangle, `a a n d b`are thelengths of sides and

1.	If in a right angled triangle, `a a n d b`are thelengths of sides and `c`is thelength of hypotenuse and `c-b!=1, c+b!=1`, then show that `(log)_("c"+"b")"a"+(log)_("c"-"b")=2(log)_("c"+"b")adot(log)_("c"-"b")adot`A. 1B. 2C. `(1)/(2)`D. none of these
Answer» Correct Answer - B Since a, b, c are the sides of a right-angled triangle with c as the largest side i.e. hypotenuse. Therefore, `c^(2) = a^(2) + b^(2)` Now, `("log"_(c+b)a + "log"_(c-b)a)/("log"_(c+b)a."log"_(c-b)a)` `= (1)/("log"_((c-b))a) + (1)/("log"_((c+b))a) = "log"_(a) (c-b) + "log"_(a) (c+b)` ` = "log"_(a) (c^(2) -b^(2)) = "log"_(a)a^(2) = 2"log"_(a)a = 2`